Let ABC be an acute angled triangle satisfying the conditions AB>BC and AC>BC. Denote by O and H the circumcentre and orthocentre, respectively, of the triangle ABC. Suppose that the circumcircle of the triangle AHC intersects the line AB at M different from A, and the circumcircle of the triangle AHB intersects the line AC at N different from A. Prove that the circumcentre of the triangle MNH lies on the line OH. geometrycircumcircleEulerincentergeometric transformationreflectiontrapezoid